The Gfan Homepage

Software package written by Anders Nedergaard Jensen

Abstract

Gfan is a software package for computing Gröbner fans and
tropical varieties. These are polyhedral fans associated to
polynomial ideals. The maximal cones of a Gröbner fan are in
bijection with the marked reduced Gröbner bases of its defining
ideal. The software computes all marked reduced Gröbner bases of an ideal. Their
union is a universal Gröbner basis. The tropical
variety of a polynomial ideal is a certain subcomplex of the
Gröbner fan. Gfan contains algorithms for computing this complex
for general ideals and specialized algorithms for tropical curves,
tropical hypersurfaces and tropical varieties of prime ideals. In
addition to the above core functions the package contains many tools
which are useful in the study of Gröbner bases, initial ideals and
tropical geometry. The full
list of commands can be found in Appendix B of the manual. For
ordinary Gröbner basis computations Gfan is not competitive in
speed compared to programs such as CoCoA, Singular and Macaulay2.

If you do not know what Gfan is you can read an old presentation of it in pdf-format or in postscript-format.
If you would like to know more please consult the manual below.
CaTS is another program for computing Gröbner fans working for toric and lattice ideals only.

Manual

Installation

Please follow the installation instructions given in Section 2 of the manual linked to above. Alternatively, go to the binaries page where you will find precompiled binaries for a small collection of operating systems. On Gentoo Linux it is even easier: Gfan can be installed using the command

sudo emerge gfan

. On other Linux distributions

sudo apt-get install gfan

might work.

License

Gfan is distributed under the terms of the GPL license version 2 or 3 as desired.

Download

Gfan version 0.6.2 (September 28th 2017, same as version 0.6.1, but with a bug fixed in the code for computing tropical starting cones.)

Gfan version 0.6.1 (September 8th 2017, same as version 0.6, but with a bug fixed in the code for computing tropical multiplicities.)

Gfan version 0.3 (October 12 2007, major update, some programs have changed behaviour, a new Polymake compatible format for polyhedral fans and polyhedral cones is supported, free choice of variable names)